In the field of Computational Fluid Dynamics, several types of mesh adaptation strategies are used to enhance a mesh’s quality, thereby improving simulation speed and accuracy. Mesh smoothing (r-refinement) is a simple and effective technique, where nodes are repositioned to increase or decrease local mesh resolution. Mesh partitioning divides a mesh into sections, for use on distributed-memory parallel machines. As a more abstract form of modeling, graph theory can be used to simulate many real-world problems, and has applications in the fields of computer science, sociology, engineering and transportation, to name a few. One of the more important graph analysis tasks involves moving through the graph to evaluate and calculate nodal connectivity. The basic structures of meshes and graphs are the same, as both rely heavily on connectivity information, representing the relationships between constituent nodes and edges. This research examines the parallelization of these algorithms using commodity graphics hardware; a low-cost tool readily available to the computing community. Not only does this research look at the benefits of the fine-grained parallelism of an individual graphics processor, but the use of Message Passing Interface (MPI) on large-scale GPUbased supercomputers is also studied.